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Sudoku techniques, from your first puzzle to expert

Every Puzzlenest sudoku has exactly one solution and can be solved without guessing. These six techniques, learned in order, are all you need for every level we publish.

A few words we'll use

  • Unit: a row, a column or a 3×3 box. Each unit holds 1 to 9 exactly once.
  • Candidates: the numbers that could still go in an empty square. Many players write them small in the corner ("pencil marks").
  • Sees: a square "sees" every other square in its row, column and box.

1. Cross-hatching (easy)

Pick a number, say 7, and a box that doesn't have a 7 yet. Look along the three rows and three columns that pass through that box. Every row or column that already contains a 7 elsewhere rules out its squares in the box. Often only one square is left. That's where the 7 goes.

Tip: Go through 1 to 9 in order, box by box. On an easy puzzle (40 starting numbers), cross-hatching alone usually solves the whole grid.

2. Naked single (easy)

Pick one empty square and list everything it sees. If it sees eight different numbers, the ninth is its answer. This works best in crowded areas of the grid.

3. Hidden single (medium)

Instead of asking "what can go in this square?", ask "where can this number go in this row?" If a row is missing a 4 and only one of its empty squares doesn't see a 4, the 4 goes there, even if that square has other candidates too. Do the same for columns and boxes.

4. Naked pair (hard)

Two squares in the same unit both have only the candidates {2, 8}. Between them they must take the 2 and the 8, so no other square in that unit can be 2 or 8. Erase those candidates from the rest of the unit. This often creates new singles.

The same works with three squares sharing three candidates (a naked triple), such as {1,5}, {5,9} and {1,9}.

5. Pointing pair (hard)

Inside one box, the only places a 6 can go are two squares in the same row. Whichever one it is, the 6 for that box is in that row. So the 6 can't appear anywhere else in that row outside the box. Erase it from those squares.

6. Box-line reduction (expert)

This is the pointing pair in reverse. In one row, the only places a 3 can go are all inside the same box. Then that box's 3 must be in that row, so erase 3 from the other squares of the box. Our expert puzzles (24 starting numbers) regularly need this step.

How to use pencil marks well

  1. Don't mark candidates until cross-hatching stops working. Early marks are mostly wasted.
  2. When you place a number, immediately erase it from the candidates of every square it sees.
  3. Look for squares with only two candidates. They form the pairs that unlock hard puzzles.

Which level should I play?

LevelStarting numbersTechniques neededTypical time
Easy401-25-10 min
Medium321-310-20 min
Hard271-520-40 min
Expert241-630+ min

Times are rough guides from our own testing. Fewer starting numbers usually means a harder puzzle, but not always: where the numbers sit matters too.

Try the techniques on today's daily sudoku. Each level has its own daily puzzle.